5. Which of the following functions grow faster than In x as x →o? Which grow at the same rate as In x? Which grow slower? b. In 2x a. log3x c. In Vx d. Vx f. 5 In x е. х g. 1/x h. e

Q: 3. Find syz for ys = In(x + yz) – xcoth-1 log ().

A: Given : Let us consider the given value as,  ys=ln(x+yz)-xcoth-1logzy

Q: Which of the following functions grow faster than In x as x→ oo? Which grow at the same rate as In…

A: fx=lnx c. gx=1x Now, limx→∞gxfx=limx→∞1xlnx=limx→∞1x lnx=0 Hence fx=lnx and gx=1x grows at same…

Q: 34. Find the area of the finite region enclosed by the curve xy 1 and line x+y= 4, leaving your…

A:

Q: The simplified form of In(÷-) using logarithmic rule is yz 4ln x+ In y- In z 4 In x- In y-In z 4ln…

A: The objective is to simplify the given expression using logarithmic rule. The given expression is

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A: Derivative of a function determines the change of variable with respect to another variable. Whereas…

Q: 2- for y = log10 e" is: dx 1 1 a) *In 10 b)- *In 10 10 In e

A: Option (a) is correct. For detail....go through the solution

Q: dy et y = (x³ – 18x)m(=). Find using the method of logarithmic dx - ifferentiation. Express your…

A: Topic:- derivatives

Q: Which of the following functions grow faster than ln x as x→∞?Which grow at the same rate as ln x?…

A: Let f(x) = ln x) and g(x) = e-x Let f(x) and g(x) be positive for x sufficiently large,  a) f(x)…

Q: Which of the following functions grow faster than ex as x→ ∞?Which grow at the same rate as ex?…

A:

Q: Find derivative for the following exponential function at x = 0 O -5 e O -5/e O 5e O 5/e

A:

Q: Which of the following functions grow faster than ln x as x→∞?Which grow at the same rate as ln x?…

A:

Q: snip

A: The exponential function and the logarithmic function is strictly increasing functions for x > 0.…

Q: Which of the following functions grow faster than ln x as x→∞?Which grow at the same rate as ln x?…

A:

Q: Suppose h(x) = log 2-. . What is the correct result of the derivative of h with respect to x? In (5)…

A: Solve for the derivative

Q: If k is a positive constant, show that x^2 e^-kx approaches 0 as x --> ∞.

A: Given  The x2e-kx approaches 0 as x→∞.Where k is a positive constant .

Q: Which of the following functions grow faster than x2 as x→∞?Which grow at the same rate as x2? Which…

A:

Q: What is the closest value to the instantaneous rate of change of the following function at x 2? f(x)…

A: We have to find closet value to the instantaneousrate of change  at x=2?     fx=3log2x-1+3   So we…

Q: Differentiate with respect to x:* y = log, (x) :() 2+ In x - In x Option 2 Option 3 2 - In x 1+ In x…

A: As per guidelines we can answer only one question at a time so if you need more answers kindly…

Q: 4. Which of the following functions grows at the same rate as ex as x goes to infinity? ex+3 e3x e2x…

A: We find which of the following functions grow at the same rate as ex as x goes to infinity: (1) ex+3…

Q: |81. Recall that the present value (PV) of an investment that pays out income continuously at a rate…

A: The present value (PV) of an investment that pays out income continuously at a rate R(t) for T years…

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A:

Q: Order the functions f(x) = log2 x, g(x) = xx , h(x) = x2 , and k(x) = 2x from the one with the…

A: Consider the given functions fx=1og2x,gx=xx,gx=x2,k=2x.

Q: The time T between calls to a call center is exponentially distributed with mean 0.2 seconds. That…

A: The exponential distribution is always related to the amount of time till a specific event occurs.…

Q: Express the guven auantity In (xt2)" single logarithm. ' + I LIn x-In (x? + 3x +a)°J as a

A:

Q: b- find x for following 1. logx = V2 2.ln(x + 1) = 5

A:

Q: Suppose that the population of a certain collection of rare Brazilian ants is given byP(t) = (t +…

A: To find the rate of change of population P'(t), we need to differentiate the function…

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A: Decay simply means the disintegration(loss of mass) of any material. If the material is radioactive…

Q: Suppose that at time t 0, 10 thousand people in a city with population 100 thousand people have…

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Q: Combine into a single logarithm. In(x – y) – 2 In(x² + y²) OIn (x-y)3 In (x²+y²)* In Va-y) (x²–y²)?…

A:

Q: - If y=a² 1-log.x and z=a* 1-log, y , then x is equal to

A: Introduction :

Q: II. Determine the derivative of the ff. logarithmic functions 1. y = 25 In 5x 2. y = -10 In 3x4 3. у…

A:

Q: 4. Which of the following functions grow faster than x2 as x→∞? Which grow at the same rate as x²?…

A:

Q: 26. Describe the behavior of each of the following: (a) 5 (b) log x as x>0 as x (c) ln x as x ->co…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: 1. Which of the following functions grow faster than e* as x→∞? Which grow at the same rate as e"?…

A: Dear students,  Please find the solutions of 3 parts. In case you need help with the other questions…

Q: Find derivative for the following exponential function at x = 0 e(x²-e5*) O -5 e O -5/e O 5e O 5/e

A: We know ddxef(x) = ef(x)·f'(x)

Q: 6. Which of the following functions grow faster than In x as x→∞? Which grow at the same rate as In…

A:

Q: d -log(z) = dz (Z

A:

Q: Find Y for the following function: dx 3- y = log,(x3- x) 4- y = In 5- tan-1 V4x – 5

A: we have to find the derivative of the following

Q: 4. Express the following single logarithm: as a i) log3 54 -log3 6 ii) 2 In (5a’b) – In (125 aº b²)…

A:

Q: Suppose a certain population is initially absent from a certain area but begins migrating there at a…

A: Consider the provided question, Suppose a certain population is initially absent from a certain area…

Q: thats a natural log of 9 to 0 and integral from 9 to e^x

A:

Q: 6) If u = log (x² + y²), then prove that log (x² CSScanned with CamScanner dydx ôxôy

A:

Q: 7. Find y'. y = log, (9– x-x)

A:

Q: 3. Find syz for ys = In(x + yz) – xcoth- log ()-

A:

Q: Which of the following functions grow faster than ln x as x→∞?Which grow at the same rate as ln x?…

A: Let f(x)=5ln x       and g(x)=ln x,

Q: A type of radioactive element has a daily radioactive decay rate of 0.5%. If 14 pounds of this…

A:

Q: 4. Suppose that the population of a certain collection of rare Brazilian ants is given by P(t) = (t…

A: Recall: Rate of change of P(t) is dP(t)dt. d(tn)dt=n.tn-1 d(u.v)dt=u.dvdt+dudt.v

Q: Solve for x (to four decimal places) in each of the following: (0.26) log25) (4x- f) (414)x (1/4)*+3…

A: (f) The given expression is,